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Stability of limit cycle in a delayed model for tumor immune system competition with negative immune response

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  • Radouane Yafia

Abstract

This paper is devoted to the study of the stability of limit cycles of a system of nonlinear delay differential equations with a discrete delay. The system arises from a model of population dynamics describing the competition between tumor and immune system with negative immune response. We study the local asymptotic stability of the unique nontrivial equilibrium of the delay equation and we show that its stability can be lost through a Hopf bifurcation. We establish an explicit algorithm for determining the direction of the Hopf bifurcation and the stability or instability of the bifurcating branch of periodic solutions, using the methods presented by Diekmann et al.

Suggested Citation

  • Radouane Yafia, 2006. "Stability of limit cycle in a delayed model for tumor immune system competition with negative immune response," Discrete Dynamics in Nature and Society, Hindawi, vol. 2006, pages 1-13, July.
    • Handle: RePEc:hin:jnddns:058463
    DOI: 10.1155/DDNS/2006/58463
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    Cited by:

    1. Gurcan, Fuat & Kartal, Senol & Ozturk, Ilhan & Bozkurt, Fatma, 2014. "Stability and bifurcation analysis of a mathematical model for tumor–immune interaction with piecewise constant arguments of delay," Chaos, Solitons & Fractals, Elsevier, vol. 68(C), pages 169-179.

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